How do weak learners become strong in boosting?
As @desertnaut mentioned in the comment

No weak learner becomes strong; it is the ensemble of the weak learners that turns out to be strong

Boosting is an ensemble method that integrates multiple models(called as weak learners) to produce a supermodel (Strong learner).

Basically boosting is to train weak learners sequentially,  each trying to correct its predecessor. For boosting, we need to specify a weak model (e.g. regression, shallow decision trees, etc.), and then we try to improve each weak learner to learn something from the data.
AdaBoost is a boosting algorithm where a decision tree with a single split is used as a weak learner. Also, we have gradient boosting and XG boosting.